Multiobjective Programming under Generalized Type I Invexity

In this paper we extend a (scalarized) generalized type-I invexity into a vector invexity (V-type I). A number of sufficiency results are established using Lagrange multiplier conditions and under various types of generalized V-type I requirements. Weak, strong, and converse duality theorems are proved in the generalized V-invexity type I setting.

[1]  Brahim Aghezzaf,et al.  Second-Order Optimality Conditions in Multiobjective Optimization Problems , 1999 .

[2]  R. Kaul,et al.  Optimality criteria and duality in multiple-objective optimization involving generalized invexity , 1994 .

[3]  R. Osuna-Gómez,et al.  Invex Functions and Generalized Convexity in Multiobjective Programming , 1998 .

[4]  L. Thibault,et al.  Lagrange multiplers for pareto nonsmooth programming problems in banach spaces , 1992 .

[5]  B. Craven.  Invex functions and constrained local minima , 1981, Bulletin of the Australian Mathematical Society.

[6]  S. Bolintinéanu,et al.  Second-Order Efficiency Conditions and Sensitivity of Efficient Points , 1998 .

[7]  Rita Pini,et al.  A survey of recent[1985-1995]advances in generalized convexity with applications to duality theory and optimality conditions , 1997 .

[8]  Miao-Ling Wang,et al.  A fuzzy multiobjective linear programming , 1997, Fuzzy Sets Syst..

[9]  R. N. Mukherjee,et al.  On generalised convex multi-objective nonsmooth programming , 1996, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10]  Shouyang Wang,et al.  Second-order necessary and sufficient conditions in multiobjective programming ∗ , 1991 .

[11]  G. Bigi,et al.  Regularity Conditions in Vector Optimization , 1999 .

[12]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .

[13]  A. Zaffaroni,et al.  Asymptotic conditions for weak and proper optimality in infinite dimensional convex vector optimization , 1996 .

[14]  M. A. Rojas-Medar,et al.  Optimally Conditions for Pareto Nonsmooth Nonconvex Programming in Banach Spaces , 1999 .

[15]  Olvi L. Mangasarian,et al.  Nonlinear Programming , 1969 .

[16]  P. Wolfe.  A duality theorem for non-linear programming , 1961 .

[17]  Zhongfei Li.  Benson Proper Efficiency in the Vector Optimization of Set-Valued Maps , 1998 .

[18]  W. Ziemba,et al.  Generalized concavity in optimization and economics , 1981 .

[19]  F. Blasco,et al.  On the Monotonicity of the Compromise Set in Multicriteria Problems , 1999 .

[20]  T. Maeda.  Constraint qualifications in multiobjective optimization problems: Differentiable case , 1994 .

[21]  M. A. Hanson,et al.  Necessary and sufficient conditions in constrained optimization , 1987, Math. Program..

[22]  M. A. Hanson.  On sufficiency of the Kuhn-Tucker conditions , 1981 .

[23]  Vaithilingam Jeyakumar,et al.  On generalised convex mathematical programming , 1992, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[24]  S. K. Mishra,et al.  Multiobjective Programming with Semilocally Convex Functions , 1996 .